The US Marine Corps is in damage control mode amid the controversy over new caps for its troops.

Marine brass flipped its lid after The Post reported Thursday that the Leathernecks, under an edict from the Obama administration, have been told to choose a “unisex” cap – known as a cover – and that a uniform advisory board was leaning away from the Marine’s iconic cover toward a style that the tough-guy troops have blasted as too feminine.

“The President in no way, shape, or form directed the Marine Corps to change our uniform cover. We are looking for a new cover for our female Marines for one overriding reason: The former manufacturer went out of business.”

But that statement flies in the face of the “voting” form sent out to Marines about the cover change.

The form, obtained by The Post, clearly instructs the troops – both male and female — to choose one cap: either the new, slim, female-friendly “Dan Daly” style or the traditional cover that Marines have sported since 1922.

“Provide a vote for either option 1 or option 2 in the appropriate row of the first column below,” the form reads. “Option 1: Adopt the Dan Daly cap as the universal cap, OR Option 2: Adopt the current male frame cap as the universal cap (with some modifications to make it more comfortable but maintain the same distinctive look).”

In an accompanying “Background Information” memo, a “uniform board” – made up of enlisted Marines — points the finger squarely at the Dept. of Defense for the new directive.

“The Marine Corps is being “encouraged” by DoD to standardize on a unisex/universal dress and service cap,” the memo reads.

“They went to the trouble of making sure the word ‘encouraged’ was in quotes,” a senior Marine source told The Post. “Clearly it is meant as a dig, to say ‘this isn’t our idea, it’s the Administration’s.’”

The internal document also noted that the “Dan Daly” style – named for the legendary Long Island Marine who was twice awarded the Medal of Honor – was initially intended as the model for an “improved female cap.” It was then “suggested, via the on-line survey process, that [it] would make an acceptable “universal” cap for all Marines.”

“None of the Working Group members liked the idea of a universal cover for all Marines. When polled, all 12 voting members of the working group voted for gender specific caps (male frame cap for male Marines and Dan Daly cap for female Marines,” the memo stated.

“The male Group members expressed a desire to maintain the current male frame cap, but agreed that it should be re-designed to improve the comfort of the cap. The Group members did not like the appearance of the Dan Daly cap on the male Marine. They said it looked like a “porter’s” cap, and couldn’t envision it with a broader crown.”

But, forced to choose one style or the other, the 10-male, 2-female board picked the Dan Daly – after the female head of the group broke a tie, according to the internal document.

“When they voted on a universal cap (either the Dan Daly cap or the male frame cap) it was a 50/50 split, with 6 members (5 males and 1 female) voting for the Dan Daly cap as the universal cap and 6 members (5 males and 1 female) voting for the male frame cap as the universal cap,” the memo noted.

“The Working Group head (a female) provided the tie breaking vote in favor of the Dan Daly cap.”

According to the documents, switching all Marines to the Dan Daly cover will cost more than $8.2 million. Adopting the traditional cap, with modifications, will save more than $284,000, because the current female covers are more expensive.

The Marines are also being asked to vote on women’s hair braids and a supplemental allowance change, according to the memo.

Meanwhile, despite the sharp denial of a cover switch on its website, USMC spokesman Capt Eric Flanagan indicated in an email to The Post Friday that the choice is between one hat — or the other.

“There is currently an ongoing survey underway asking Marines about their preferences on which type of cover they prefer,” he wrote. “The results of the survey will assist the uniform board in making the final decision.”

About 7 percent of Marines are women, according to recent statistics.

“If the Marine Corps has ‘zero intention’ of changing the male cover, then why did they go to the time and expense to create a prototype male Dan Daly cover? Why bring in at least four Marines to model them for the photographs, in two different uniform combinations?” said the senior Marine source. “Why have the Uniform Board vote on adopting the Dan Daly?”